Multiple choice

The A.M of two positive numbers is 40 and their G.M is 24, the numbers are

  1. 72, 8

  2. 70, 10

  3. 60, 20

  4. None of these
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A Correct answer
Explanation

For two numbers x and y: AM = (x+y)/2 = 40, so x + y = 80. GM = √(xy) = 24, so xy = 576. We can find (x-y)^2 = (x+y)^2 - 4xy = 6400 - 2304 = 4096, so x-y = 64. Solving x + y = 80 and x - y = 64 gives x = 72, y = 8.

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